CONTROL AND RECOVERY FROM RARE CONGESTION EVENTS IN A LARGE MULTISERVER SYSTEM

We develop deterministic fluid approximations to describe the recovery from rare congestion events in a large multi-server system in which c ustomer holding times have a general distribution. There are two cases , depending on whether or not we exploit the age distribution (the dis tribution of elapsed holding times of customers in service). If we do not exploit the age distribution, then the rare congestion event is a large number of customers present. If we do exploit the age distributi on, then the rare event is an unusual age distribution, possibly accom panied by a large number of customers present. As an approximation, we represent the large multi-server system as an M/G/infinity model. We prove that, under regularity conditions, the fluid approximations are asymptotically correct as the arrival rate increases. The fluid approx imations show the impact upon the recovery time of the holding-time di stribution beyond its mean. The recovery time may or not be affected b y the holding-time distribution having a long tail, depending on the p recise definition of recovery. The fluid approximations can be used to analyze various overload control schemes, such as reducing the arriva l rate or interrupting services in progress. We also establish large d eviations principles to show that the two kinds of rare events have th e same exponentially small order. We give numerical examples showing t he effect of the holding-time distribution and the age distribution, f ocusing especially on the consequences of long-tail distributions.